Times, Events, and Censoring

library(tibble)

library(dplyr)

library(foreign)

library(pander)

1 Introduction

Think about a hypothetical event: e.g. birth, death, partnering, marriage or commitment to a partner, entering a program, leaving a program, attaining a degree, first diagnosis of anxiety or depression, etc.

2 Simulate Data

set.seed(2779) # random seed

N <- 10 # sample size

T <- 10 # number of timepoints

id <- rep(seq(1, N), each = T) # id's 1 to N

t <- rep(seq(1, T), N) # timepoints 1 to T

# random event times

# uniform event times

event_time <- rep(round(runif(N, 3, T), 
                        digits = 0), 
                  each = T)

event <- t >= event_time # event has occurred t >= event_time

event <- factor(event, 
                levels = c(FALSE, TRUE), 
                labels = c("No Event", "Event"))

# arbitrarily censored after 7

censored <- event_time > 7 

censored <- factor(censored, 
                   levels = c(FALSE, TRUE), 
                   labels = c("Not Censored", "Censored"))

# tibble

# data required for animation

mydata <- tibble::tibble(id, t, event_time, event, censored)

mydata2 <- mydata %>%
  filter(t == 1) %>%
  select(id, event_time, censored)

write.dta(mydata, file = "event-history-multiple-records.dta")

write.dta(mydata2, file = "event-history-single-record.dta")

3 Animated Graph

library(ggplot2)

library(plotly)

Individuals in the animation below who have not yet experienced an event are indicated by a ●.

When an event occurs for an individual, the symbol changes to a ×.

In this simulation, we imagine that the study period ends after time 7, so observations for which the event occurs after time 7 are considered to be censored: i.e. a failure is not observed.

Censored observations (failure not observed) are maize ⬤, and non-censored observations (failure observed) are blue ⬤ .

pal <- c("#00274C", "#FFCB05") # color palette

p2 <- plot_ly(data = mydata, # use mydata
              x = ~t, # x is t (time)
              y = ~id, # y is id
              frame = ~t, # frames based on t (time)
              text = ~paste("Event:" ,
                            event,
                            "<br>Censored:",
                            censored),
              type = 'scatter',
              mode = 'marker',
              color = ~censored, # color is censored (yes / no)
              colors = pal, # use color palette
              symbol = ~as.numeric(event), # symbol is event (occurred / not occurred)
              symbols = c('circle', # event not occurred
                          'x'), # event
              marker = list(size = 10)) %>% # marker size
  layout(title = 'Hypothetical Timing of Events \nCensored at Time 7',
         shapes = list(type='line', # censoring line
                       x0 = 7, 
                       x1 = 7, 
                       y0 = 0, 
                       y1 = 10, 
                       line=list(dash='dot', 
                                 width=1, 
                                 color = "red"))) %>%
  animation_opts(3000) 

p2 # replay

4 What These Data Look Like

library(DT)

4.1 Simple Event History Data

datatable(mydata2, caption = "Simple Event History Data")

4.2 Data in Multiple Record Form

Notice how every row in this particular data set is a person timepoint, not simply a person. Every person in this data has multiple rows.

datatable(mydata, caption = "Data in Multiple Record Form")

4.3 Survival Curve

use "event-history-single-record.dta"

stset event_time, failure(censored == 1) // set event time and failvar

sts graph, xline(7, lcolor("red")) // survival curve w line at 7

graph export survival.png, replace

(Written by R.              )


Survival-time data settings

         Failure event: censored==1
Observed time interval: (0, event_time]
     Exit on or before: failure

--------------------------------------------------------------------------
         10  total observations
          0  exclusions
--------------------------------------------------------------------------
         10  observations remaining, representing
          5  failures in single-record/single-failure data
         71  total analysis time at risk and under observation
                                                At risk from t =         0
                                     Earliest observed entry t =         0
                                          Last observed exit t =        10

        Failure _d: censored==1
  Analysis time _t: event_time

file
    /Users/agrogan/Desktop/GitHub/newstuff/categorical/survival-analysis-and-event-hi
    > story/survival.png saved as PNG format

Survival Graph